Model order reduction (MOR) is a technique used to reduce the order of system models under analysis by simplifying overly complex aspects of the system. The reduced order system model is a good approximation that possesses the key properties and maintains fidelity to the original system model. In order to create good representative models for analysis, algorithms used for reducing model order must be efficient and accurate. Model order reduction typically demands a good understanding of inputs and outputs to the system, the purpose of analysis, the level of fidelity required for the analysis and the efficiency of the analysis obtained by the model order reduction.
In the realm of electronic design automation (EDA), current MOR methods work well on system models having a small number of externally connected terminals, commonly termed “ports”. As more ports are added to a system model, the size of the network also increases. As more internal nodes are added to the system model, the size of the network gets even bigger. Due to the complexity of the system model, current model order reduction methods cannot handle the size of the network exceeding ten million nodes. Two major approaches have been taken to resolve the issues associated with the network size: projection-based methods and elimination-based methods.
Projection-based methods are suitable for system models with a small number of ports. Since both the CPU and memory requirements scale quadratically to the number of ports, projection-based methods are not well suited for system models with many ports. In addition, in most cases, projection methods for model order reduction are of similar complexity, meaning that the reduced system matrices might be still too dense to benefit from computational advantages. The order of the reduced model is at least equal to and generally larger than the number of ports.
Elimination-based methods eliminate a number of nodes that have little or no interest during simulation. As an example, an RC network is reduced by eliminating internal nodes via steps of approximation and simplification. Elimination-based methods reduce the order of the system by elimination of the internal nodes but still have difficulties with a large number of nodes with large time constants, for example, power grid networks with device capacitors. Elimination-based methods may result in over simplification or incorrect representation of the original system model.